Combines spatial context priors with data term for better dendritic spine segmentation.
problem Poor segmentation results due to overlapping pixel intensity distributions.
method Combines nonparametric context priors with learned-intensity data term and nonparametric shape priors.
result Significant improvements in dendritic spine segmentation.
Natural gradient learning improves synaptic plasticity in spiking neurons.
problem Parametrization dependence leads to inconsistencies in classical synaptic plasticity theories.
method Proposes natural gradient descent in Riemannian geometry for spiking neurons.
result Derives a synaptic learning rule that explains biological phenomena.
Novel data acquisition schemes have been an emerging need for scanning microscopy based imaging techniques to reduce the time in data acquisition and to minimize probing radiation in sample exposure. Varies sparse sampling schemes have been studied and are ideally suited for such applications where the images can be re…
We give a short answer to the question in the title: {\em dendrits}. Precisely we show that the C∗-algebra C(X) of all complex-valued continuous functions on a compactum X is projective in the category C1 of all (not necessarily commutative) unital C∗-algebras if and only if X is a…
New spines found in complex 4D shapes.
problem Finding spines in complex 4D shapes.
method Examined Levine and Lidman's constructions and found new spines.
result Infinitely many 4-manifolds have topological spines.
Single neuron with ADA learns XOR and outperforms other functions.
problem Classifying linearly non-separable data.
method Proposed a new artificial neuron with apical dendrite activation.
result ADA function achieves 100% accuracy on XOR and superior performance on benchmark datasets.
Paper proves unique contact structure supported by positive flow-spines.
problem Existence and uniqueness of contact structures on 3-manifolds.
method Introduces positivity condition for flow-spines and proves existence and uniqueness of contact structures.
result Any positive flow-spine of a closed, connected, oriented 3-manifold supports a unique contact structure up to isotopy.
Nonpositive towers property in 3-manifolds spines.
problem Properties of 3-manifold spines.
method Analysis of 2-dimensional spines in aspherical 3-manifolds and 3-ball.
result Nonpositive towers property in 2-dimensional spines of aspherical 3-manifolds.
Calcium imaging permits optical measurement of neural activity. Since intracellular calcium concentration is an indirect measurement of neural activity, computational tools are necessary to infer the true underlying spiking activity from fluorescence measurements. Bayesian model inversion can be used to solve this prob…
In this paper we raise the question whether every closed Riemannian manifold has a spine of minimal area, and we answer it affirmatively in the surface case. On constant curvature surfaces we introduce the spine systole, a continuous real function on moduli space that measures the minimal length of a spine in each surf…
We show that a compact n-polyhedron PL embeds in a product of n trees if and only if it collapses onto an (n-1)-polyhedron. If the n-polyhedron is contractible and n\ne 3 (or n=3 and the Andrews-Curtis Conjecture holds), the product of trees may be assumed to collapse onto the image of the embedding. In contrast, there…
Unique simple spines of homotopy 2-spheres are shown to be ambiently isotopic.
problem Characterizing and comparing simple spines of homotopy 2-spheres.
method Proving ambient isotopy of simple spines representing the same homology class.
result Simple spines of homotopy 2-spheres are unique.
Bing's house-like spines approximate all PL manifolds.
problem Understanding spines of PL manifolds.
method Approximation rigidity and h-principle.
result PL manifolds have spines similar to Bing's house.
Corrects a 1-off error in Harer's spine dimension calculation for decorated Teichmüller spaces.
problem Incorrect dimension calculation in Harer's spine for decorated Teichmüller spaces.
method Identifies and corrects the dimension discrepancy in Harer's spine construction.
result Corrects the dimension of Harer's spine by 1 for decorated Teichmüller spaces.
Constructs Teichmüller curve to study Thurston spine structure.
problem Understanding the structure of Thurston spine in Teichmüller space.
method Constructs a Teichmüller curve and characterizes its intersection with Thurston spine.
result Characterizes Thurston spine as a trivalent tree and equivariant deformation retract of Teichmüller curve.
This paper proves a map from flow-spines to contact structures is surjective.
problem Mapping flow-spines to contact structures in 3-manifolds.
method Using positive flow-spines and contact structures, proving surjectivity.
result The map from flow-spines to contact structures is surjective.
The Thurston spine's properties are studied in relation to Morse-Smale complexes.
problem Understanding the Thurston spine's local properties and their global implications.
method Analyzes the Thurston spine as a subset of Teichmüller space and studies its local properties in relation to the systole function.
result The Thurston spine satisfies properties analogous to Morse-Smale complexes, demonstrating its topological significance.
Trees emerge from group boundaries in hyperbolic geometry.
problem Understanding boundaries of hyperbolic groups and their maps.
method Analyzing short exact sequences of hyperbolic groups and their boundaries.
result The quotient of H boundary by ending laminations is a dendrite.
In this article we establish the relation between the spines of 3-manifolds and the polyhedra with identified faces. We do this by showing that the spines of the closed, connected, orientable 3-manifolds can be presented through polyhedra with identified faces in a very natural way. We also prove the equivalence betwee…
A special spine of a three-manifold is said to be poor if it does not contain proper simple subpolyhedra. Using the Turaev-Viro invariants, we establish that every compact three-dimensional manifold M with connected nonempty boundary has a finite number of poor special spines. Moreover, all poor special spines of the m…
The abstract extends Reidemeister theorem to 3-manifolds using diagrams of links and bands.
problem Extending Reidemeister theorem to 3-manifolds.
method Defines diagrams for links and bands on spines and flow-spines of 3-manifolds and describes combinatorial moves.
result Reproves and extends Brand et al. result on 3-manifolds.
New geometric spine for Artin groups defined by cube complexes.
problem Geometric characterization of Artin group spines.
method Category of spatial cube complexes for geometric simplicial complex.
result Realized spine as natural simplicial complex.
Paper shows mapping class group-equivariant Teichmüller space deformation to Thurston spine.
problem Mapping Teichmüller space to Thurston spine.
method Equivariant deformation retraction of Teichmüller space onto a cell complex.
result Thurston spine contains points corresponding to hyperbolic surfaces with shortest geodesics forming polygons.
Thurston's spine dimension exceeds virtual cohomological dimension.
problem Understanding the dimension of Thurston's spine in moduli space.
method Analyzing closed hyperbolic surfaces and their systoles.
result The dimension of the set of surfaces is at least \(5-\varepsilon\) for large genus.
A spine is constructed for a non-orientable surface's decorated Teichmüller space.
problem Constructing a spine for a non-orientable surface's decorated Teichmüller space.
method Building on Harer's work, constructing a spine and computing its dimension, showing equivariance with the pure mapping class group.
result A spine is constructed with minimal dimension for a punctured non-orientable surface.
New 3-manifold spines with unique Whitehead graphs identified.
problem Identifying new 3-manifold spines with specific Whitehead graph types.
method Cyclic presentations and conditions on parameters to show spines of 3-manifolds.
result Examples of 3-manifolds with Whitehead graphs of specific types.
The paper shows conditions under which certain 4-manifolds have no smooth spines.
problem Conditions for 4-manifolds to have no smooth spines.
method Using Heegaard Floer homology and high-dimensional surgery theory, the paper identifies obstructions for 4-manifolds to have smooth spines.
result The paper proves that certain knots and 4-manifolds do not have smooth spines.
Theory of link projections to 3-manifold spines, proving combinatorial moves for isotopic links.
problem Link equivalence on 3-manifold spines.
method Theory of link projections, combinatorial moves, Reidemeister Theorem.
result Crossingless projections and combinatorial moves for isotopic links.
Study of projective Fraïssé limits of trees with confluent epimorphisms.
problem Finite trees with monotone epimorphisms do not amalgamate.
method Developed new mappings and properties of continua to apply to topological graphs.
result Topological realization of the Fraïssé limit of finite trees with ramification vertices of order at most 3 is the Wa\. zewski dendrite D3. Hippocampal dentate granule cells are among the few neuronal cell types generated throughout adult life in mammals. In the normal brain, new granule cells are generated from progenitors in the subgranular zone and integrate in a typical fashion. During the development of epilepsy, granule cell integration is profoundly…
Any bounding compact smooth manifold bounds a compact manifold with a spine consisting of transversely intersecting codimension one submanifolds. This paper provides details for a picture proof given in previous papers with S. Akbulut.
Simplified combinatorial descriptions of branched spines for 3-manifolds using primary MP move and sliding moves.
problem Combinatorial descriptions of branched spines for 3-manifolds and their equivalence relations.
method Demonstrated that 16 MP moves on branched spines are derived from a primary MP move, pure sliding moves, and their inverses.
result Simpler combinatorial descriptions for closed 3-manifolds and combed 3-manifolds.
Outer space and Teichmüller space fail well-rounded retract analogy.
problem Failure of well-rounded retract in Outer space and Teichmüller space.
method Analysed flat tori and metric graphs to show failure.
result Analogue of well-rounded retract does not contain equivariant spine.
Labyrinth fractals are self-similar dendrites in the unit square that are defined with the help of a labyrinth set or a labyrinth pattern. In the case when the fractal is generated by a horizontally and vertically blocked pattern, the arc between any two points in the fractal has infinite length [Cristea\&Steinsky 2009…
Geometrical spines are defined for 3-manifolds with natural metrics, in particular, for lens manifolds. We show that any spine of L(p,q) close enough to its geometrical spine (i.e., to the cut locus with respect to the standard metric) contains at least E(p,q)-3 vertices, which is exactly the conjectured value for Matv…
2-stratifolds are a generalization of 2-manifolds in that there are disjoint simple closed branch curves. We obtain a list of all closed 3-manifolds that have a 2-stratifold as a spine.
Study shows bounds on symplectic fillings for spinal open book decompositions.
problem Understanding symplectic fillings of contact 3-manifolds.
method Introduced spine removal surgery operation to prove universal bounds.
result Proves a universal bound on the Euler characteristic and signature of minimal symplectic fillings.
New proof confirms surfaces can be divided into polygons.
problem Estimating the dimension of Thurston spine.
method Existence of an infinite set A, proving codimension is o(g/ log g).
result Proves recent conjecture about Thurston spine dimension.
Continuum-wise hyperbolicity is exactly the pseudo-Anosov dynamics with spine singularities.
problem Classification of continuum-wise hyperbolic surface homeomorphisms
method Proving a complete structural classification
result Every cwF-hyperbolic homeomorphism is pseudo-Anosov with spine singularities We establish a calculus for branched spines of 3-manifolds by means of branched Matveev-Piergallini moves and branched bubble-moves. We briefly indicate some of its possible applications in the study and definition of State-Sum Quantum Invariants.
This note popularizes a proof for 3-manifold triangulations and spines.
problem Connecting triangulations of 3-manifolds with specific moves.
method Dual viewpoints of triangulations and spines; combinatorial proof replacing general position arguments.
result Unified proof for both closed and non-compact 3-manifolds.
We introduce and analyze the characteristic foliation induced by a contact structure on a branched surface, in particular a branched standard spine of a 3-manifold. We extend to (fairly general) singular foliations of branched surfaces the local existence and uniqueness results which hold for genuine surfaces. Moreover…
The paper studies curves in surfaces using flow-spines and apparent contours.
problem Understanding curves in arbitrary surfaces using flow-spines and apparent contours.
method By considering generic curves and their apparent contours relative to a traversing flow, the paper reconstructs curves and allows them to vary up to homotopy.
result A finite set of local moves on decorated graphs allows for the reconstruction and variation of curves within a fixed generic flow.
Study shows how activation functions impact the storage capacity of treelike neural networks.
problem Understanding the role of activation functions in neural network expressive power.
method Analysis of treelike two-layer networks with various activation functions in the infinite-width limit.
result Activation functions affect storage capacity and robustness, with nonlinearity increasing capacity and decreasing robustness.
New contractible complex shows virtual cohomological dimension of RAAGs.
problem Determining virtual cohomological dimension of RAAGs.
method Equivariant deformation retraction of spine to contractible cube complex.
result Dimension of new complex realises virtual cohomological dimension of RAAGs.
For a 3-dimensional manifold M3, its complexity c(M3), introduced by S.Matveev, is the minimal number of vertices of an almost simple spine of M3; in many cases it is equal to the minimal number of tetrahedra in a singular triangulation of M3. An approach to estimating c(M3) from below for total spaces o…
We show that under reasonable conditions, the spines of the handlebodies of a strongly irreducible Heegaard splitting will intersect a closed ball in a graph which is isotopic into the boundary of the ball. This is in some sense a generalization of the results by Scharlemann on how a strongly irreducible Heegaard split…
We introduce a novel approach for predicting the progression of adolescent idiopathic scoliosis from 3D spine models reconstructed from biplanar X-ray images. Recent progress in machine learning have allowed to improve classification and prognosis rates, but lack a probabilistic framework to measure uncertainty in the …